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MTU GE 4250 - Properties of Radiation

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2/12/14%1%Properties of Radiation Lecture outline • Flux and intensity • Solid angle and the steradian • Inverse square law • Global insolation • Interaction of radiation with matter What’s this? SEVIRI sensor High-resolution visible (HRV) image Meteosat Second Generation (MSG) Geostationary satellite 15 Feb 2013, central Russia2/12/14%2%Flux or Flux density • Flux (or flux density), F: rate at which radiation is incident on, or passes through, a flat surface (e.g., the ground, the top of a cloud layer, a level in the atmosphere…); Units: W m-2 • By definition, a broadband quantity integrated between wavelength limits (λ1 and λ2) • Spectral flux (or monochromatic flux ): flux contributed by radiation over some narrow wavelength interval; Units: W m-2 µm-1 • e.g., the incident flux of solar radiation on an area of Earth’s surface • No information on direction of origin Intensity or radiance • Radiant intensity or radiance, I: describes both the strength and direction of radiation sources contributing to the flux incident on a surface; Units: W m-2 sr-1 (Watts per square meter per steradian) • Roughly corresponds to ‘brightness’ of a radiation source – e.g., the sky, clouds, the Sun. Remote sensing instruments, e.g., a satellite sensor viewing a narrow range of directions, measure radiance Spectral radiance: intensity measured over some narrow wavelength interval; Units: W m-2 sr-1 µm-12/12/14%3%Spherical polar coordinates • Direction plays an important role in any discussion of radiation θ = zenith angle, usually relative to local vertical θ = 0º is overhead, θ = 90º is the horizon. Φ = azimuth angle, e.g., the direction of the sun Solid angle: the steradian • Three-dimensional analog of the planar radian (ratio of arc length:radius) • Ω = area of surface A / r2 (NB. Solid angle is dimensionless) • Sphere subtends a solid angle of … sr • The entire sky (hemisphere) above the horizon subtends … sr • Sun seen from Earth covers ~0.00006 sr How much of the visual field of view is occupied by an object? 1 steradian2/12/14%4%Solid angle: the steradian • sin θ accounts for the convergence of ‘longitude’ lines at the ‘pole’ € dω4π∫= sinθdθdφ= 2πsinθdθ0π∫0π∫02π∫= 4πSolid angle problem • Mean distance of the moon from Earth = 3.84 x 105 km • Radius of the moon = 1.74 x 103 km • Mean distance of the Sun from Earth = 1.496 x 108 km • Radius of the Sun = 6.96 x 105 km • What is the angular diameter subtended by the Sun and moon? • What is the solid angle subtended by the Sun and moon? • Which appears larger from the Earth?2/12/14%5%Solid angle problem Geometric framework for calculating the solid angle subtended by a sphere of radius R whose center is a distance D from the observer Solid angle problem (a) θmax = 2 sin-1 (R/D); Moon = 0.52º Sun = 0.53º (b) Solid angle of a cone with apex angle 2θ: € sinθdθdφ= 2πsinθdθ0θ∫0θ∫02π∫= 2π−cosθ[ ]0θ= 2π(1− cosθ)Moon: 6.5×10-5 Sun: 6.8×10-5 (c) Sun subtends a solid angle 5% larger than the moon If these values were constant, could total solar eclipses be explained?2/12/14%6%Formal definition of intensity • Flux (F; measured on a surface normal to the beam) per unit solid angle (ω) traveling in a particular direction • Typical units: Watts per square meter per steradian (W m-2 sr-1) • Conservation of intensity: intensity (radiance) does not decrease with distance from the source (within a vacuum or other transparent medium) • Contrast with flux density € ˆ Ω € Iˆ Ω ( )=δFδωInverse square law • Irradiance (or flux density) decreases as the square of distance from the source • Radiance is invariant with distance (note dependence of solid angle on r2) • Solar ‘constant’ (irradiance at top of Earth’s atmosphere) is ~1370 W m-2 Flux density at surface of sphere F F F F flux2/12/14%7%Global insolation • How much total solar radiation Φ is incident on Earth’s atmosphere? • Consider the amount of radiation intercepted by the Earth’s disk 1370 W m-2 € Φ = S0πRE2= 1.74 ×1017W• Applies for mean Sun-Earth distance of 1.496 x 108 km • But Earth’s orbit is elliptical, so the solar flux (S) actually varies from 1330 W m-2 in July to 1420 W m-2 in January Global insolation • In addition to Earth’s orbit, the power output from the Sun also varies over time (e.g., sunspot cycles) • Furthermore, radiation is not uniformly incident on the surface but varies with incidence angle of the Sun Houghton Where is the peak? Note that this shows the amount of radiation incident at the top of the atmosphere only, not that which is available for absorption by the surface and atmosphere2/12/14%8%Relationship between flux and intensity • Flux (F): total power incident on a unit surface area • Intensity (I): Flux contribution arriving from small element of solid angle along a direction The flux density of radiation carried by a beam in the direction Ω through a surface element dA is proportional to cos θ = € ˆ n ⋅ˆ Ω • Hence, flux incident on or emerging from an arbitrary surface is found by integrating I over all relevant solid angles • Since intensity is defined as the flux per unit solid angle normal to the beam, the contributions to the flux must be weighted by a factor of cos θ € ˆ Ω Relationship between flux and intensity • The upward-directed flux from a surface is therefore given by: € F↑= I cosθdω=02π∫I↑(θ,φ)cosθsinθdθdφ0π/ 2∫02π∫• What is the flux density of isotropic radiation? (i.e., if intensity is constant) € F↑= I↑(θ,φ)cosθsinθdθdφ0π/ 2∫02π∫= 2π I cosθsinθdθ0π / 2∫= 2π I12sin 2θdθ0π / 2∫= πIe.g., illumination of a horizontal surface under heavily overcast skies2/12/14%9%Radiative properties of natural surfaces • Illumination of the atmosphere from below by ‘upwelling’ radiation Geological mapping Landsat-8 Operational Land Imager (OLI) July 30, 2013 Xinjiang province, NW China http://earthobservatory.nasa.gov/IOTD/view.php?id=82853 Why the different colors?2/12/14%10%Atmospheric windows The fate of incident radiation • Radiation incident on a surface is either reflected, absorbed or transmitted • Conservation of energy dictates that the


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